# Functional Elements — Tolerances and Fits

---

## 1. Rolling Bearings (ISO 286-1 + ISO 15 / ISO 76)

### Fundamental principle
The ring that **rotates relative to the load direction** must have **interference** with its seat.
If the load-carrying ring can slip in its seat, "creep" begins: progressive erosion, vibration
and premature failure.

### Fixed end / free end scheme (thermal expansion)

```
          Fixed end (FE)               Free end (FL)
Shaft:    k5 / m5  (interference)      h6  (deliberate clearance)
Housing:  H7   (clearance)             G7 / H7  (clearance)

    ┌────────────────────────────────────────────────────┐
    │  [Bearing FE]  ═══ shaft ═══  [Bearing FL]         │
    │   k5 / H7                    h6 / H7 or G7         │
    └────────────────────────────────────────────────────┘
    FE: locked axially               FL: free to slide
    (outer ring retained             (outer ring free to move
     by shoulder/Seeger ring)         in bore for thermal growth)
```

> The free end exists because the shaft grows thermally: without it, parasitic axial loads
> build up and destroy bearings and structure.

### Tolerance table — Ball and roller bearings (class P0/P6)

#### SHAFT seat (inner ring)

| Condition | d ≤ 18 mm | 18 < d ≤ 100 mm | 100 < d ≤ 200 mm | Notes |
|---|---|---|---|---|
| Light / variable load | h5, js5 | h6, js6 | h6 | Easy to disassemble |
| **Normal load** (motors, gearboxes) | **k5** | **k5, m5** | **m6, n6** | Industrial standard |
| Heavy load / impact | m5, n5 | m5, n5, p5 | n6, p6 | Thermal assembly |
| Pure axial thrust | js5, h5 | js6, h6 | h6 | No load rotation |
| Free end | h6 | h6 | h6 | Deliberate clearance for thermal growth |

#### HOUSING seat (outer ring)

| Condition | Bore tolerance | Notes |
|---|---|---|
| Fixed outer ring, rotating load on shaft | **H7** | Standard — removable |
| Impact loads / vibrations | **JS7, K7** | Slight interference |
| Rotating outer ring (wheels, idler pulleys) | **N7, M7** | Interference — non-removable |
| Heavy loads with rotating outer ring | **P7** | Strong interference |
| Adjustable or frequently removable support | **G7** | Deliberate clearance |

### Precision bearings (class P5, P4, P2)

| Class | Shaft | Housing | Application |
|---|---|---|---|
| P5 | j5, k5 | H6, JS6 | Simple spindles, precision pumps |
| P4 | j5, k4 | H5, JS5 | Machine tool spindles |
| P2 | j4, k4 | H4 | High-precision grinders, measuring machines |

### Angular contact bearings (matched pair)

For O (back-to-back) or X (face-to-face) mounting with preload:
- Shaft: js5 or k5 (maintains axial preload)
- Housing: JS6 (for controlled preload) or H7 standard
- ⚠️ Avoid heavy interference: it reduces the bearing's internal preload

### Bearing seat roughness

| Element | Ra | Rz | Notes |
|---|---|---|---|
| Shaft (P0/P6) | ≤ 0.8 µm | ≤ 4 µm | Cylindrical grinding required |
| Housing (P0/P6) | ≤ 1.6 µm | ≤ 8 µm | Fine boring or internal grinding |
| Shaft (P5/P4) | ≤ 0.4 µm | ≤ 2 µm | Precision grinding |
| Shoulder / axial abutment | ≤ 1.6 µm | — | Flatness important (± 0.005 mm) |

### Practical rules for common machines

| Machine | Shaft (inner ring) | Housing (outer ring) |
|---|---|---|
| Electric motor (drive side) | m5 | H7 |
| Electric motor (free end) | k5 | H7 |
| Industrial gearbox | k5 or m5 | H7 or JS7 |
| Centrifugal pump | k5 or m5 | H7 |
| Fan (vibrations) | m5 | JS7 |
| Wheel / idler pulley | h6 | N7 or M7 |
| Machine tool spindle | j5 or k5 | H6 or JS6 |

---

## 2. Gears

### Gear bore – shaft fit

| Requirement | Fit | Torque path | Notes |
|---|---|---|---|
| Removable, frequent maintenance | H7/h6 + key | Key only | Small clearance, cold-removable |
| Removable, infrequent maintenance | H7/k6 + key | Key + slight interference | **Industrial standard** |
| Hot-removable, high precision | H7/m6 + key | Key + medium interference | Heat to 80–120°C |
| Fixed, moderate torque | H7/p6 | Interference only | No key → no stress concentration |
| Fixed, high torque | H7/r6 or s6 | Interference only | Thermal assembly mandatory |
| High angular precision | H6/k5 + key | Key | Minimises run-out |

### Tooth profile quality (ISO 1328-1)

| Quality | Application | Indicative tooth IT | Finishing process |
|---|---|---|---|
| 3–5 | Measurement, instruments | IT5–IT6 | Profile grinding |
| 6–7 | Machine tools, precision gearboxes | IT6–IT7 | Grinding or shaving |
| 8–9 | Industrial gearboxes | IT7–IT8 | Shaving / hobbing |
| 10–11 | General mechanics | IT9–IT10 | Hobbing only |
| 12 | Toys, low speed | IT11–IT12 | Rough hobbing |

### Centre distance tolerance (ISO 1328)

| Application | Tolerance | IT grade (indicative) |
|---|---|---|
| Precision gearboxes | ±0.01 – 0.02 mm | IT6–IT7 |
| Industrial gearboxes | ±0.03 – 0.05 mm | IT8–IT9 |
| General mechanics | ±0.1 mm | IT10–IT11 |

---

## 3. Valve Seats

### Internal combustion engine valves

| Component | Typical material | Fit | Notes |
|---|---|---|---|
| Exhaust valve seat insert | Sintered steel | H7/s6 – H7/u6 | High interference: retains at operating Δt (up to 300°C) |
| Intake valve seat insert | Cast iron or sintered | H7/r6 – H7/s6 | Medium interference |
| Valve guide | Bronze or sintered | H7/p6 or H7/r6 (OD) + D9/f7 (ID) | External fix + stem clearance |
| Valve stem in guide | Nitrided steel | D9/f7 or G8/f7 | Clearance 0.03–0.08 mm (intake) 0.05–0.10 mm (exhaust) |

### Pneumatic / hydraulic valves

| Type | Fit | Required Ra | Notes |
|---|---|---|---|
| Fixed seat (press in) | H7/r6 – H7/s6 | Ra ≤ 0.8 µm (seat) | Seal by interference + optional sealant |
| Spool / slide valve | H7/f7 – H7/g6 | **Ra ≤ 0.4 µm** | Gap 0.01–0.05 mm critical for leakage |
| Piston rod / stem | H8/f7 | Ra ≤ 0.8 µm | Combined with O-ring or lip seal |
| High-pressure piston (no seal) | H6/g5 | Ra ≤ 0.2 µm | Metal-to-metal seal — gap 3–8 µm |

---

## 4. Transmission Shafts — Complete Layout

### Functional zone map

```
     ┌────┬──────────┬──────┬──────────┬──────┬──────────┬────┐
     │ FE │ bearing  │ non  │  gear    │ non  │ bearing  │ FL │
     │    │ (k5/m5)  │ func │  (k6/p6) │ func │  (h6)    │    │
     └────┴──────────┴──────┴──────────┴──────┴──────────┴────┘
      ↑                                                      ↑
   fixed end                                           free end
   (axial load locked)                         (free to slide axially)
```

### Tolerance table by shaft zone

| Functional zone | Shaft tolerance | Ra | Element |
|---|---|---|---|
| Bearing seat — fixed end | k5 or m5 | ≤ 0.8 µm | Bearing inner ring |
| Bearing seat — free end | h6 | ≤ 0.8 µm | Bearing inner ring (slides) |
| Removable gear seat | k6 | ≤ 1.6 µm | Gear + key N9 |
| Fixed gear seat | p6 | ≤ 0.8 µm | Gear (interference) |
| Lip seal seat (simmering) | h11 or h8 | **0.2–0.4 µm** | Rubber/PTFE lip |
| Seeger ring groove on shaft | h11 (groove diameter) | ≤ 3.2 µm | Snap ring |
| Keyway width | N9 | ≤ 3.2 µm | DIN 6885 key |
| Non-functional zones / fillets | h9 – h11 | ≤ 6.3 µm | — |
| Threaded end | 6g (thread) | — | Locking nut |

---

## 5. Keys (DIN 6885-1 / ISO 773)

→ For dimension tables, fit types, clearance calculation and torque check: see `keys-keyways.md`

### Fit summary

| Fit type | Shaft keyway | Hub keyway | Key | Use |
|---|---|---|---|---|
| Normal | N9 | JS9 | h9 | **Industrial standard** |
| Sliding | H9 | D10 | h9 | Hub slides axially |
| Tight | P9 | P9 | h9 | No clearance, high precision |

> ⚠️ The keyway is a stress concentration feature that reduces shaft fatigue strength
> by 25–40%. Do not position at zones of maximum bending.

---

## 6. Snap Rings — Seeger (DIN 471 / DIN 472)

### Types
- **DIN 471**: ring for **shaft** (opens to mount in external groove)
- **DIN 472**: ring for **bore** (closes to mount in internal groove)

### Groove tolerances

#### DIN 471 — Groove on SHAFT

| Shaft diameter d (mm) | Groove width b | Tolerance b | Groove diameter d1 | Tolerance d1 |
|---|---|---|---|---|
| 6 – 9 | 0.9 | h13 | d − 1.0 | h11 |
| 9 – 19 | 1.0 | h13 | d − 1.1 | h11 |
| 19 – 28 | 1.2 | h13 | d − 1.3 | h11 |
| 28 – 46 | 1.5 | h13 | d − 1.65 | h11 |
| 46 – 80 | 1.75 | h13 | d − 1.95 | h11 |
| 80 – 100 | 2.0 | h13 | d − 2.25 | h11 |

#### DIN 472 — Groove in BORE (housing)

| Bore diameter D (mm) | Groove width b | Tolerance b | Groove diameter D1 | Tolerance D1 |
|---|---|---|---|---|
| 8 – 14 | 1.0 | H13 | D + 1.0 | H11 |
| 14 – 22 | 1.1 | H13 | D + 1.2 | H11 |
| 22 – 38 | 1.2 | H13 | D + 1.3 | H11 |
| 38 – 65 | 1.5 | H13 | D + 1.6 | H11 |
| 65 – 100 | 1.8 | H13 | D + 2.0 | H11 |
| 100 – 120 | 2.0 | H13 | D + 2.2 | H11 |

### Practical rules
- The H11/h11 groove is intentionally wide to allow ring installation with pliers
- Groove diameter controls axial load capacity: always verify against ring load rating (SKF/Seeger tables)
- Groove root radius: r ≤ 0.2 mm to prevent ring jamming
- Do not use Seeger rings for alternating or impact axial loads: use a shoulder or nut

---

## 7. Cylindrical and Tapered Pins (ISO 8734 / ISO 8735 / ISO 2339)

### Cylindrical pins (ISO 8734 — hardened steel, ISO 8735 — with extraction thread)

| Function | Pin–bore fit | Notes |
|---|---|---|
| Fixed locating / torque pin | **H7/n6** | Interference — press fit, non-removable |
| Fixed pin with extraction (ISO 8735) | **H7/n6** | Same, but removable with extractor |
| Removable locating pin | **H7/g6** | Controlled clearance — hand-removable |
| Hinge / pivot pin | **H7/f7** | Clearance for rotation — lubrication recommended |

### Tapered pins (ISO 2339 — taper 1:50)
- Self-locking: retained by elastic deformation — no special tolerance needed
- Bore produced by **reaming with tapered reamer** after assembly (recommended)
- Disadvantage: bore is not interchangeable — each pin is matched to its bore

### Locating hole position (GD&T)

```
TP_bore ≤ 0.5 × min_clearance  (for locating pins)
TP_bore ≤ 0.3 × min_interference  (for fixed pins)
```

---

## 8. Plain Bearings / Bushings

### Types and materials

| Type | Material | Characteristic | Outer fit (in housing) |
|---|---|---|---|
| Bronze bushing | CuSn8, CuZn24Al | High load capacity, lubrication required | **H7/s6 or H7/u6** |
| Sintered self-lubricating | Fe or Cu sintered | Impregnated lubrication, low speed | **H7/r6 or H7/s6** |
| PTFE / graphite bushing | PTFE composite | Dry, low speed, high temperature | **H7/p6 or H7/r6** |
| Bimetal (steel + bronze) | St + CuSn | High load capacity | **H7/s6** |
| Nylon / POM bushing | Polyamide, POM | Lightweight, low torque, quiet | **H7/p6** (check thermal Δt) |

### Inner fit: bushing bore – shaft

| Condition | Fit | Indicative clearance | Notes |
|---|---|---|---|
| Continuous rotation, lubricated | H7/f7 or H8/f7 | 0.02–0.07 mm (Ø50) | Standard — clearance for oil film |
| High speed, forced lubrication | H7/g6 | 0.01–0.05 mm (Ø50) | More stable hydrodynamic film |
| Oscillating (no full rotation) | H9/f9 or H9/e9 | 0.04–0.12 mm (Ø50) | More clearance to avoid stick-slip |
| Very light load, low speed | H8/h8 | 0–0.054 mm (Ø50) | Near zero clearance, marginal lubrication |

### Note on plastic bushings (POM/PA)
Plastics have 5–10× higher thermal expansion than steel.
- At ambient temperature: use recommended fit
- At operating temperature: verify interference does not generate excessive pressure (hub cracking
  risk) and that internal clearance does not become negative (seizure)
- Rule of thumb: for POM with Δt = +50°C on Ø30, allow 0.06 mm additional clearance

---

## 9. Radial Shaft Seals / Lip Seals (DIN 3760 / ISO 6194)

### Seat tolerances

| Element | Tolerance | Ra | Notes |
|---|---|---|---|
| **Shaft** (lip contact surface) | **h11** or **h8** | **Ra 0.2–0.4 µm** | Circumferential texture — NOT helical |
| Housing bore (seal press-in) | **H8** | Ra 1.6–3.2 µm | Lead-in chamfer at entry (15°, r=0.3 mm) |

### Lip material and speed limits

| Lip material | Max speed (m/s) | Temperature range | Notes |
|---|---|---|---|
| NBR (nitrile) | ≤ 6 m/s | −40 / +100°C | Standard — mineral oil |
| FKM (Viton) | ≤ 9 m/s | −20 / +180°C | Synthetic oil, high temperature |
| PTFE | ≤ 15 m/s | −60 / +200°C | Low friction, marginal lubrication |
| PTFE with stainless lip | ≤ 20 m/s | −60 / +200°C | High speed |

### Critical requirements

1. **Shaft hardness**: min 55 HRC (or surface treatment: nitriding, chrome plating)
   — Soft shaft → lip cuts surface within hours → seal failure
2. **Circumferential finish**: texture must be perpendicular to axis
   — Axial grinding direction: lip pumps fluid outward (screw effect → leaks)
3. **Shaft eccentricity (TIR)**: max 0.1–0.2 mm depending on diameter and speed
4. **Internal pressure**: standard seals up to 0.3 bar; above → reinforced spring seal or double lip

---

## 10. Locating and Positioning Pins

### Self-locking taper pins
- Taper 1:50 (ISO 2339 standard): self-locking, suitable for moderate torque
- Taper 1:30 (DIN 1): used on tooling, easier to remove
- Extraction slot in head is always recommended

### Spring pins (ISO 8752)

| Application | Notes |
|---|---|
| Light positioning, low torque | Economical, bore tolerance H12 — easy assembly |
| Replaces solid pin in vibrating environments | Spring elasticity absorbs vibrations |

### Locating pins for flanges and plates
- Standard: 2 pins diametrically opposed (no more — redundancy creates GD&T issues)
- Diameter: 6–12 mm for most industrial cases
- Fit: H7/n6 on both bores (matched plates) or H7/g6 if frequently removed

---

## 11. Involute Splines (ISO 4156 / DIN 5480)

For applications requiring:
- High torque (> 500 Nm on shafts Ø < 50 mm)
- Frequent reversals (no angular backlash)
- High-precision angular connections that must be removable

### Fit classes (ISO 4156)

| Class | Application | Notes |
|---|---|---|
| **H/h** (clearance) | Removable, axially sliding | Standard for couplings |
| **H/js** (transition) | Precise positioning, fixed | Light press |
| **H/k, H/m** (interference) | Fixed, high torque | Same as solid hub fits |

> Do not dimension individual teeth: use the full ISO 4156 designation
> (e.g. "DIN 5480 W30×2×14×9H/9h") and reference the standard.

---

## 12. Couplings

### Rigid couplings (sleeves, discs)

| Condition | Shaft–coupling fit | Notes |
|---|---|---|
| Fixed, removable | H7/k6 + key | Light press, hot-removable |
| Fixed, non-removable | H7/p6 or r6 | Interference — thermal assembly |
| Precision (no angular play) | H6/k5 | High precision |

### Flexible couplings (spider, elastomer)
- Shaft–hub fit: H7/k6 or H7/m6
- Clearance compensated by elastic element — heavy interference not needed
- Misalignment tolerance: see manufacturer's data sheet (typical: 0.1–0.5 mm radial, 0.5–2° angular)

### Oldham and universal (cardan) joints
- Shaft–hub: H7/g6 or H7/h6 + pin or key
- Centre element must slide: female side of joint H7/f7 – H8/f8

---

## 13. Linear Guides and Sliding Surfaces

| Guide type | Fit | Ra | Application |
|---|---|---|---|
| Sliding guide, lubricated | H7/f7 | ≤ 0.8 µm | Machine tools, cylinders |
| Sliding guide, high precision | H6/g5 | ≤ 0.4 µm | Measuring machines |
| Guide pin / die column | H7/g6 | ≤ 0.8 µm | Dies, fixtures |
| Zero-clearance guide (preloaded) | H6/h5 + preload | ≤ 0.4 µm | Precision tables |
| Taper centering (self-locating) | — | ≤ 0.8 µm | Taper 1:50–1:100, no ISO tolerance needed |

---

## 14. General Tolerances (ISO 2768)

For non-critical dimensions, use general tolerances rather than tolerancing every dimension.

| Class | Symbol | Approx. grade | Application |
|---|---|---|---|
| Fine | f | IT9–IT10 | Precision mechanics |
| **Medium** | **m** | **IT11** | **Industrial standard (default)** |
| Coarse | c | IT12–IT13 | Structures, fabrications |
| Very coarse | v | IT14–IT15 | Raw castings, forgings |

**Drawing note**: `ISO 2768-mK` (medium linear + medium geometric tolerances)

---

## Appendix: Quick Decision Flowchart

```
What is the function of the fit?
│
├─ Must SLIDE / ROTATE? ─────────────────────────→ Clearance
│   ├─ High precision, lubricated  → H7/g6 or H6/g5
│   ├─ Standard, lubricated        → H7/f7 or H8/f7
│   └─ Loose, misalignment         → H8/e8 or H9/d9
│
├─ Must LOCATE (removable)? ─────────────────────→ Transition / zero clearance
│   ├─ High precision               → H6/h5 or H7/js6
│   └─ Standard                     → H7/h6 or H7/k6
│
├─ Must TRANSMIT TORQUE (fixed)? ────────────────→ Interference
│   ├─ Removable with tools          → H7/k6 + key
│   ├─ Moderate torque               → H7/p6
│   ├─ High torque                   → H7/r6 or H7/s6
│   └─ Maximum (bronze/cast iron)    → H7/u6
│
├─ Is it a BEARING? ──────────────────────────────→ see §1
├─ Is it a KEY / KEYWAY? ─────────────────────────→ see §5 / keys-keyways.md
├─ Is it a SEEGER / SNAP RING? ───────────────────→ see §6
├─ Is it a PIN? ──────────────────────────────────→ see §7
├─ Is it a BUSHING? ──────────────────────────────→ see §8
├─ Is it a LIP SEAL / SIMMERING? ─────────────────→ see §9
└─ Is it a SPLINED PROFILE? ──────────────────────→ see §11
```